Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... Formulas for Oblique - angled Triangles , .... 90-98 Solution of Oblique - angled Triangles , 98-116 MENSURATION . Mensuration Defined , .. The Area of a Parallelogram , The Area of a Triangle ,. Formula for the Sine and Cosine of Half ...
... Formulas for Oblique - angled Triangles , .... 90-98 Solution of Oblique - angled Triangles , 98-116 MENSURATION . Mensuration Defined , .. The Area of a Parallelogram , The Area of a Triangle ,. Formula for the Sine and Cosine of Half ...
Page 218
... :: AB3 : ab3 ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homolo- gous lines . GENERAL FORMULAS . If we denote the volume of any 218 GEOMETRY .
... :: AB3 : ab3 ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homolo- gous lines . GENERAL FORMULAS . If we denote the volume of any 218 GEOMETRY .
Page 219
... FORMULAS . If we denote the volume of any prism by V , its base by B , and its altitude by H , we shall have ( P. XIV . ) , V = B x H • • ( 1. ) If we denote the volume of any pyramid by V , its base by B , and its altitude by H , we ...
... FORMULAS . If we denote the volume of any prism by V , its base by B , and its altitude by H , we shall have ( P. XIV . ) , V = B x H • • ( 1. ) If we denote the volume of any pyramid by V , its base by B , and its altitude by H , we ...
Page 246
... FORMULAS . If we denote the convex surface of a cylinder by S , its volume by V , the radius of its base by R , and its alti- tude by H , we have ( P. I. , II . ) , S 2πR X H - V = TR2 x H • ( 1. ) ( 2. ) If we denote the convex surface ...
... FORMULAS . If we denote the convex surface of a cylinder by S , its volume by V , the radius of its base by R , and its alti- tude by H , we have ( P. I. , II . ) , S 2πR X H - V = TR2 x H • ( 1. ) ( 2. ) If we denote the convex surface ...
Page 28
... formulas into ordinary language , we have the following PRINCIPLES . 1. The perpendicular of any right - angled triangle is equal to the hypothenuse multiplied by the sine of the angle at the base . 2. The base is equal to the ...
... formulas into ordinary language , we have the following PRINCIPLES . 1. The perpendicular of any right - angled triangle is equal to the hypothenuse multiplied by the sine of the angle at the base . 2. The base is equal to the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence